Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-3x+3y &= -1 \\ 6x+6y &= -9\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = -6x-9$ Divide both sides by $6$ to isolate $y$ $y = {-x - \dfrac{3}{2}}$ Substitute this expression for $y$ in the first equation. $-3x+3({-x - \dfrac{3}{2}}) = -1$ $-3x - 3x - \dfrac{9}{2} = -1$ Simplify by combining terms, then solve for $x$ $-6x - \dfrac{9}{2} = -1$ $-6x = \dfrac{7}{2}$ $x = -\dfrac{7}{12}$ Substitute $-\dfrac{7}{12}$ for $x$ back into the top equation. $-3( -\dfrac{7}{12})+3y = -1$ $\dfrac{7}{4}+3y = -1$ $3y = -\dfrac{11}{4}$ $y = -\dfrac{11}{12}$ The solution is $\enspace x = -\dfrac{7}{12}, \enspace y = -\dfrac{11}{12}$.